Internal rotation kinetic energy operator

In summary, the internal rotation kinetic energy operator is a mathematical expression used in quantum mechanics to describe the rotational motion of molecules. It takes into account the mass and moment of inertia of the molecule, as well as the angular momentum and the square of the angular velocity. The operator is crucial in understanding the behavior of molecules in various states and environments, and is often used in the study of molecular dynamics and spectroscopy. Its calculation involves the use of complex integrals and can provide valuable insights into the structure and properties of molecules.
  • #1
Konte
90
1
Hello everybody,

My question today is:
Given a molecule that has an internal degree of liberty ( let's take the ethane molecule with its internal rotation as an example), how to write the kinetic energy operator by means of the corresponding internal coordinate?

Thank you guys.

Konte
 
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  • #3
DrClaude said:
It depends on the internal degree of freedom. Rotation of polyatomic molecules involves angular momenta operators along each of the principle axes of inertia, usually rewritten in terms of the total angular momentum operator.

See, e.g., http://tiger.chem.uw.edu.pl/staff/tania/WykladyBJ/Wyklad_ENG_9.pdf

Thank you for answer.
 

FAQ: Internal rotation kinetic energy operator

1. What is the Internal Rotation Kinetic Energy Operator?

The Internal Rotation Kinetic Energy Operator is a mathematical operator in quantum mechanics that describes the rotational energy of a molecule or system of particles. It is used to calculate the energy of a molecule's internal rotational motion, which is important in understanding its structure and behavior.

2. How is the Internal Rotation Kinetic Energy Operator calculated?

The Internal Rotation Kinetic Energy Operator is calculated by taking the second derivative of the wave function with respect to the internal rotation coordinates. This involves using the position and momentum operators for the internal rotation coordinates, and applying the Schrödinger equation to solve for the energy of the system.

3. What is the significance of the Internal Rotation Kinetic Energy Operator in quantum mechanics?

The Internal Rotation Kinetic Energy Operator is significant in quantum mechanics because it helps us understand the behavior of molecules and systems of particles. It allows us to calculate the energy associated with internal rotational motion, which is important in predicting the behavior of molecules and their interactions with other particles.

4. How does the Internal Rotation Kinetic Energy Operator relate to other kinetic energy operators?

The Internal Rotation Kinetic Energy Operator is a specific type of kinetic energy operator, which describes the energy associated with rotational motion. It is related to other kinetic energy operators, such as the translational and vibrational kinetic energy operators, which describe the energy associated with different types of motion of a molecule or system of particles.

5. What are some applications of the Internal Rotation Kinetic Energy Operator?

The Internal Rotation Kinetic Energy Operator has many applications in chemistry and physics. It is used in spectroscopy to analyze the rotational energy levels of molecules, in molecular dynamics simulations to study the behavior of molecules, and in quantum chemistry calculations to predict molecular properties. It is also important in understanding chemical reactions and molecular interactions.

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